To clean dirty greasy hands, slobber lots of skin lotion onto them, work it around, and then wipe it off onto a rag. Most of the dirty grease will come off with the lotion.
Technique demonstrated by Star.
To make it work even better, before starting your dirty work, rub lots of lotion into your hands .
Especially work it under your nails. In the cleanup phase, an old toothbrush works great for cleaning fingernails.
Step 1: Work It In
The lotion contains emulsifiers such as lecithin that make it possible for oil and water to mix.
So the wet lotion greedily mixes with the dirty grease and loosens it from your hands.
Step 2: Wipe With Rag
It helps if you sing your favorite car mechanic song while you do this.
Step 3: Clean!
Repeat as necessary, and if you're a real cleanliness freak you can proceed to a sink to continue the process with soap and water.
It doesn't much matter what kind of lotion you use, probably the cheaper the better.
It might work with butter also, please report back if that works for you.